To find the weighted average of the numbers -1 and 1, with a weight of [tex]\(\frac{2}{3}\)[/tex] on the first number and [tex]\(\frac{1}{3}\)[/tex] on the second number, follow these steps:
1. Identify the numbers and their respective weights:
- The first number is [tex]\(-1\)[/tex] with a weight of [tex]\(\frac{2}{3}\)[/tex].
- The second number is [tex]\(1\)[/tex] with a weight of [tex]\(\frac{1}{3}\)[/tex].
2. Multiply each number by its weight:
- For the first number:
[tex]\[
-1 \times \frac{2}{3} = -\frac{2}{3}
\][/tex]
- For the second number:
[tex]\[
1 \times \frac{1}{3} = \frac{1}{3}
\][/tex]
3. Sum the weighted values:
[tex]\[
-\frac{2}{3} + \frac{1}{3} = -\frac{2}{3} + \frac{1}{3} = -\frac{1}{3}
\][/tex]
Thus, the weighted average of the numbers [tex]\(-1\)[/tex] and [tex]\(1\)[/tex], with the specified weights, is [tex]\(-\frac{1}{3}\)[/tex] or approximately -0.3333333333333333.
